# Quantum chaos in a Bose-Hubbard dimer with modulated tunnelling

## TL;DR

This paper investigates quantum chaos in a Bose-Hubbard dimer with modulated tunnelling, using numerical simulations and statistical measures to distinguish chaotic from regular quantum dynamics, and demonstrates the effectiveness of the truncated Wigner approximation.

## Contribution

It introduces the statistical distance between number distributions as a new measure to identify chaos in quantum dynamics of the Bose-Hubbard dimer.

## Key findings

- Statistical distance effectively distinguishes chaotic from regular quantum states.
- Truncated Wigner approximation accurately captures beyond mean-field dynamics.
- Chaotic regions exhibit irregular Wigner functions, yet are well-represented by the method.

## Abstract

In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics.